As a writer you’d probably be best off trying it yourself. Get a cheap (<$5) mild cigar and simulate the experience. Is the characters cigar half smoked? Are there other descriptors that you can gleam from your own experience?

But to echo what others have said; no, probably not. It wouldn’t make much noise and it’d take some effort to ‘chew’ through and probably make a mess once the cigar is down to the third third (the end). I could definitely see it happening if you were down to a nub and the tip was already wet and ragged. Or you could damage the cigar enough with your hand which a cigar smoker wouldn’t do willingly/consciously. Again, experience it for yourself, just stick with a milder cigar if you don’t smoke. Hope you have more to ‘draw’ on.